中文摘要：

深入透彻地了解振动信号的频谱结构，有助于通过简单易行的频谱分析对行星齿轮箱进行故障诊断。考虑齿轮制造误差和分布式故障对啮合振动的调幅调频作用、以及行星轮通过效应对振动测试信号的调幅作用，建立了行星齿轮箱正常和分布式故障状态下的振动信号模型，推导了频谱解析表达式。给出了太阳轮、行星轮和齿圈分布式故障特征频率的计算公式。通过实验信号分析验证了上述理论分析结果，基于频谱分析诊断了自然产生发展的齿轮分布式故障。

英文摘要：

A thorough understanding of the vibration signal spectral structure is helpful for fault diagnosis of planetary gearboxes via common yet effective spectral analysis. Considering both the amplitude modulation and the frequency modulation effects due to gear manufacturing errors or distributed faults, as well as the amplitude modulation caused by the passing effect of planets, signal models of normal and distributed fault cases and their Fourier transforms were given, and the spectral characteristics were summarized in closed form. Meanwhile, explicit equations for calculating the characteristic frequency of distributed gear fault were deduced. The theoretical derivations were validated using experimental datasets. According to the theoretical derivations, the naturally developed gear fault in a planetary gearbox was detected and located.